An original real-coded genetic algorithm methodology that has been developed for the estimation of the parameters of the Tarver reactive flow model of shock initiation and detonation of heterogeneous solid explosives is described in detail. This methodology allows, in a single optimisation procedure and without the need for a starting solution, to search for the 15 parameters of the reaction rate law of the reactive flow model that fit the numerical results to the experimental ones. The developed methodology was applied and tested with an experimental situation, described in detail in the literature, involving the acceleration of a tantalum metal plate by an LX-17 explosive charge. The obtained parameters allow a very good description of the experimental results and are close to the ones originally used by Tarver and co-authors in their simulation of the phenomenon.